The most persistent soft-clique in a set of sampled graphs

When searching for characteristic subpatterns in potentially noisy graph data, it appears self-evident that having multiple observations would be better than having just one. However, it turns out that the inconsistencies introduced when different graph instances have different edge sets pose a serious challenge. In this work we address this challenge for the problem of finding maximum weighted cliques. We introduce the concept of most persistent soft-clique. This is subset of vertices, that 1) is almost fully or at least densely connected, 2) occurs in all or almost all graph instances, and 3) has the maximum weight. We present a measure of clique-ness, that essentially counts the number of edge missing to make a subset of vertices into a clique. With this measure, we show that the problem of finding the most persistent soft-clique problem can be cast either as: a) a max-min two person game optimization problem, or b) a min-min soft margin optimization problem. Both formulations lead to the same solution when using a partial Lagrangian method to solve the optimization problems. By experiments on synthetic data and on real social network data we show that the proposed method is able to reliably find soft cliques in graph data, even if that is distorted by random noise or unreliable observations. Copyright 2012 by the author(s)/owner(s).

Random function priors for exchangeable arrays with applications to graphs and relational data

A fundamental problem in the analysis of structured relational data like graphs, networks, databases, and matrices is to extract a summary of the common structure underlying relations between individual entities. Relational data are typically encoded in the form of arrays; invariance to the ordering of rows and columns corresponds to exchangeable arrays. Results in probability theory due to Aldous, Hoover and Kallenberg show that exchangeable arrays can be represented in terms of a random measurable function which constitutes the natural model parameter in a Bayesian model. We obtain a flexible yet simple Bayesian nonparametric model by placing a Gaussian process prior on the parameter function. Efficient inference utilises elliptical slice sampling combined with a random sparse approximation to the Gaussian process. We demonstrate applications of the model to network data and clarify its relation to models in the literature, several of which emerge as special cases.

Model reductions for inference: generality of pairwise, binary, and planar factor graphs.

We offer a solution to the problem of efficiently translating algorithms between different types of discrete statistical model. We investigate the expressive power of three classes of model-those with binary variables, with pairwise factors, and with planar topology-as well as their four intersections. We formalize a notion of "simple reduction" for the problem of inferring marginal probabilities and consider whether it is possible to "simply reduce" marginal inference from general discrete factor graphs to factor graphs in each of these seven subclasses. We characterize the reducibility of each class, showing in particular that the class of binary pairwise factor graphs is able to simply reduce only positive models. We also exhibit a continuous "spectral reduction" based on polynomial interpolation, which overcomes this limitation. Experiments assess the performance of standard approximate inference algorithms on the outputs of our reductions.

A sustainable PWR fuel cycle with complete TRU recycling using fertile-free fuel

The feasibility of a conventional PWR fuel cycle with complete recycling of TRU elements in the same reactor is investigated. A new Combined Non-fertile and Uranium (CONFU) fuel assembly where about 20% of the uranium fuel pins are replaced with fertile free fuel (FFF) hosting TRU generated in the previous cycle is proposed. In this sustainable fuel cycle based on the CONFU fuel assembly concept, the amount and radiotoxicity of the nuclear waste can be significantly reduced in comparison with the conventional once-through UO 2 fuel cycle. It is shown that under the constraints of acceptable power peaking limits, the CONFU assembly exhibits negative reactivity feedback coefficients comparable in values to those of the reference UO2 fuel. Moreover, the effective delayed neutron fraction is about the same as for UO2-fueled cores. Therefore, feasibility of the PWR core operation and control with complete TRU recycle has been shown in principle. However, gradual build up of small amounts of Cm and Cf challenges fuel reprocessing and fabrication due to the high spontaneous fissions rates of these nuclides and heat generation by some Pu, Am, and Cm isotopes. Feasibility of the processing steps becomes more attainable if the time between discharge and reprocessing is 20 years or longer. The implications for the entire fuel cycle will have to be addressed in future studies.